I can pick any one and CC connects just fine. I only have one instance of Calibre running on my computer.

I'm not sure what this means, and it's a minor thing, but I'm curious.

In the past with other hardware this has happened to me. This means your computer that has calibre running on it is connected to your network via a wire and wireless connection. Since your computer is connected to your network two ways, CC sees two calibre instances to choose from.

I had this happen with a video streaming app and connecting to the wireless vs the wired made a difference since the bandwidth required on the network for the video was so large. Most likely picking either won't make a difference to you since the data bandwidth required for calibre is relatively low.

You can fix this by disabling the wireless when you are connected to your wired network.

I'm confused. I didn't have my phone wired connected to my computer and thence to calibre that way. I had the wifi on on the phone, and the wireless device connected through the connect/share icon. I don't see how that could be two instances, and I'm not sure how to disable the wireless.

I'm confused. I didn't have my phone wired connected to my computer and thence to calibre that way. I had the wifi on on the phone, and the wireless device connected through the connect/share icon. I don't see how that could be two instances, and I'm not sure how to disable the wireless.

as i say, it's a small thing, but potentially confusing.

I wasn't referring to your phone. In my previous experience it was my computer that was connected to my network via two methods. If this isn't your experience I can't explain it other than to say it is a problem outside of calibre or CC's control.

I'm confused. I didn't have my phone wired connected to my computer and thence to calibre that way. I had the wifi on on the phone, and the wireless device connected through the connect/share icon. I don't see how that could be two instances, and I'm not sure how to disable the wireless.

as i say, it's a small thing, but potentially confusing.

He didn't say that you had a phone connected to your computer. He said that (possibly) your computer has both a network cable plugged in and also wireless turned on. This is in general not a good idea because as far as the network is concerned, your computer is there twice. Lots of things can get confused.

Does your computer have wifi? If so, what happens if you turn it off? If dwanthny is correct, and I think he is, then after turning off wifi you will see only one calibre from CC. In addition, your computer's networking performance could improve. Cabled connections are far preferable to wifi connections.

If your computer has both a cabled connection and a wifi connection and for some reason you want to leave wifi on, then you should probably unplug the cable. Alternatively, your computer might have some setting that tells it to automatically disable wifi when a cable is plugged in. I have no idea where such a setting might be, if it exists at all.

My computer has wifi, but it's hard-wired in. I do have a wireless mouse - could that be causing the duplication?

Your mouse has nothing to do with it. If your computer's wifi is active and connecting to your wireless router along with your computer being wired then your CC will see two paths (one wired and one wireless) to your calibre install and report seeing two instances. Check out all of the icons in your task bar, one probably shows you connected via wifi. Disabling the wifi connection (on your computer) will remove the duplicate instance of calibre that CC sees.

If this is a laptop you take on the road be aware that you will have to re-enable wifi if you want to link via wireless away from your house.